A340965 Number of ways to write n as an ordered sum of 9 primes.

1, 9, 36, 93, 198, 387, 696, 1170, 1845, 2740, 3960, 5562, 7566, 10125, 13248, 17133, 22014, 27774, 34776, 43173, 53010, 64869, 78696, 94617, 113415, 134946, 159552, 188164, 219960, 256041, 297180, 342846, 394614, 452595, 516276, 587997, 667938, 755109, 852444

Offset: 18

Author

Ilya Gutkovskiy, Jan 31 2021

Keywords

• nonn

Links

• Seiichi Manyama, Table of n, a(n) for n = 18..10000

Crossrefs

Column k=9 of A121303.

Cf. A000040, A010051, A073610, A098238, A259200, A340960, A340961, A340962, A340963, A340964, A340966.

Programs

Maple

b:= proc(n, k) option remember; local r, p; r, p:= 0, 2;
      if n=0 then `if`(k=0, 1, 0) elif k<1 then 0 else
      while p<=n do r:= r+b(n-p, k-1); p:= nextprime(p) od; r fi
    end:
a:= n-> b(n, 9):
seq(a(n), n=18..56);  # Alois P. Heinz, Jan 31 2021

Mathematica

nmax = 56; CoefficientList[Series[Sum[x^Prime[k], {k, 1, nmax}]^9, {x, 0, nmax}], x] // Drop[#, 18] &

Formula

G.f.: (Sum_{k>=1} x^prime(k))^9.